% Mizar problem: t43_realset3,realset3,734,49 
fof(t43_realset3,conjecture,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] : 
              ( m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
             => ! [D] : 
                  ( m1_subset_1(D,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                 => k1_funct_1(k2_realset3(A),k4_tarski(B,k1_funct_1(k5_realset2(A),k4_tarski(C,D)))) = k1_funct_1(k2_realset3(A),k4_tarski(k1_funct_1(k2_realset3(A),k4_tarski(B,C)),D)) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_realset1,cc1_relset_1,d2_realset3,d4_xboole_0,dt_k1_funct_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_realset2,dt_k2_realset3,dt_k2_zfmisc_1,dt_k4_realset2,dt_k4_tarski,dt_k4_xboole_0,dt_k5_realset1,dt_k5_realset2,dt_k8_funct_2,dt_k8_realset2,dt_l1_group_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l1_vectsp_1,dt_l2_struct_0,dt_l2_vectsp_1,dt_l3_vectsp_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m3_realset1,dt_m4_realset1,existence_l1_group_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_l1_vectsp_1,existence_l2_struct_0,existence_l2_vectsp_1,existence_l3_vectsp_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m3_realset1,existence_m4_realset1,fc3_realset1,fc4_realset1,rc1_realset1,rc2_realset1,rc3_realset1,redefinition_k5_realset1,redefinition_k8_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t23_realset2,t28_realset2,t2_subset,t30_realset3,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,t6_boole,t6_realset3,t7_boole,t8_boole]),
    [file(realset3,t43_realset3)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ~ v1_xboole_0(A) ) ),
    file(realset1,cc1_realset1),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(d2_realset3,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k2_realset2(A),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))),k2_realset2(A))
            & m2_relset_1(B,k2_zfmisc_1(k2_realset2(A),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))),k2_realset2(A)) )
         => ( B = k2_realset3(A)
          <=> ! [C] : 
                ( m1_subset_1(C,k2_realset2(A))
               => ! [D] : 
                    ( m1_subset_1(D,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                   => k1_funct_1(B,k4_tarski(C,D)) = k1_funct_1(k5_realset2(A),k4_tarski(C,k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),D))) ) ) ) ) ) ),
    file(realset3,d2_realset3),
    []).

fof(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_realset2,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ~ v1_realset1(k2_realset2(A)) ) ),
    file(realset2,k2_realset2),
    []).

fof(dt_k2_realset3,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ( v1_funct_1(k2_realset3(A))
        & v1_funct_2(k2_realset3(A),k2_zfmisc_1(k2_realset2(A),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))),k2_realset2(A))
        & m2_relset_1(k2_realset3(A),k2_zfmisc_1(k2_realset2(A),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))),k2_realset2(A)) ) ) ),
    file(realset3,k2_realset3),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k4_realset2,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => m1_subset_1(k4_realset2(A),k2_realset2(A)) ) ),
    file(realset2,k4_realset2),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_realset1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_realset1(A)
        & m1_subset_1(B,A) )
     => m4_realset1(k5_realset1(A,B),A) ) ),
    file(realset1,k5_realset1),
    []).

fof(dt_k5_realset2,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => m3_realset1(k5_realset2(A),k2_realset2(A),k4_realset2(A)) ) ),
    file(realset2,k5_realset2),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(dt_k8_realset2,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ( v1_funct_1(k8_realset2(A))
        & v1_funct_2(k8_realset2(A),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
        & m2_relset_1(k8_realset2(A),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) ) ) ),
    file(realset2,k8_realset2),
    []).

fof(dt_l1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => l1_struct_0(A) ) ),
    file(group_1,l1_group_1),
    []).

fof(dt_l1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => l2_struct_0(A) ) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l1_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => l1_group_1(A) ) ),
    file(vectsp_1,l1_vectsp_1),
    []).

fof(dt_l2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => l1_struct_0(A) ) ),
    file(struct_0,l2_struct_0),
    []).

fof(dt_l2_vectsp_1,axiom,(
    ! [A] : 
      ( l2_vectsp_1(A)
     => ( l1_vectsp_1(A)
        & l2_struct_0(A) ) ) ),
    file(vectsp_1,l2_vectsp_1),
    []).

fof(dt_l3_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( l1_rlvect_1(A)
        & l2_vectsp_1(A) ) ) ),
    file(vectsp_1,l3_vectsp_1),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_m3_realset1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,A)
     => ! [C] : 
          ( m3_realset1(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,k2_zfmisc_1(A,A),A)
            & m2_relset_1(C,k2_zfmisc_1(A,A),A) ) ) ) ),
    file(realset1,m3_realset1),
    []).

fof(dt_m4_realset1,axiom,(
    $true ),
    file(realset1,m4_realset1),
    []).

fof(existence_l1_group_1,axiom,(
    ? [A] : l1_group_1(A) ),
    file(group_1,l1_group_1),
    []).

fof(existence_l1_rlvect_1,axiom,(
    ? [A] : l1_rlvect_1(A) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l1_vectsp_1,axiom,(
    ? [A] : l1_vectsp_1(A) ),
    file(vectsp_1,l1_vectsp_1),
    []).

fof(existence_l2_struct_0,axiom,(
    ? [A] : l2_struct_0(A) ),
    file(struct_0,l2_struct_0),
    []).

fof(existence_l2_vectsp_1,axiom,(
    ? [A] : l2_vectsp_1(A) ),
    file(vectsp_1,l2_vectsp_1),
    []).

fof(existence_l3_vectsp_1,axiom,(
    ? [A] : l3_vectsp_1(A) ),
    file(vectsp_1,l3_vectsp_1),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(existence_m3_realset1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,A)
     => ? [C] : m3_realset1(C,A,B) ) ),
    file(realset1,m3_realset1),
    []).

fof(existence_m4_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ? [B] : m4_realset1(B,A) ) ),
    file(realset1,m4_realset1),
    []).

fof(fc3_realset1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A))
      & v1_realset1(k1_tarski(A)) ) ),
    file(realset1,fc3_realset1),
    []).

fof(fc4_realset1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_realset1(A)
        & m4_realset1(B,A) )
     => ~ v1_xboole_0(k4_xboole_0(A,B)) ) ),
    file(realset1,fc4_realset1),
    []).

fof(rc1_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(realset1,rc1_realset1),
    []).

fof(rc2_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_realset1(A) ) ),
    file(realset1,rc2_realset1),
    []).

fof(rc3_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ? [B] : 
          ( m4_realset1(B,A)
          & ~ v1_xboole_0(B) ) ) ),
    file(realset1,rc3_realset1),
    []).

fof(redefinition_k5_realset1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_realset1(A)
        & m1_subset_1(B,A) )
     => k5_realset1(A,B) = k1_tarski(B) ) ),
    file(realset1,k5_realset1),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t23_realset2,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] : 
              ( m1_subset_1(C,k2_realset2(A))
             => ! [D] : 
                  ( m1_subset_1(D,k2_realset2(A))
                 => k1_funct_1(k5_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),D)) = k1_funct_1(k5_realset2(A),k4_tarski(B,k1_funct_1(k5_realset2(A),k4_tarski(C,D)))) ) ) ) ) ),
    file(realset2,t23_realset2),
    []).

fof(t28_realset2,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
         => ! [C] : 
              ( m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
             => ( m1_subset_1(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                & m1_subset_1(k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),B),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) ) ) ) ) ),
    file(realset2,t28_realset2),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t30_realset3,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] : 
              ( m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
             => m1_subset_1(k1_funct_1(k2_realset3(A),k4_tarski(B,C)),k2_realset2(A)) ) ) ) ),
    file(realset3,t30_realset3),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t6_realset3,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
         => ! [C] : 
              ( m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
             => k1_funct_1(k8_realset2(A),k1_funct_1(k5_realset2(A),k4_tarski(B,C))) = k1_funct_1(k5_realset2(A),k4_tarski(k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),B),k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),C))) ) ) ) ),
    file(realset3,t6_realset3),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).